In this paper we present JPEG steganography method based on hiding data to the stream of ternary coefficients. In the proposed method each nonzero DCT coefficient is converted to the corresponding ternary coefficient. The block of 3m − 1 ternary coefficients is used for hiding m ternary messages by modifying one or two coefficients. Due to higher information density of the ternary coefficients, the proposed method has many solutions for hiding necessary data. Such a big choice enables to choose coefficients with lowest distortion impact. As a result, the proposed methods have better data hiding performance compared to the existing steganographic methods based on hiding data to stream of binary coefficients like matrix encoding (F5) and modified matrix encoding (MME). The proposed methods were tested with steganalysis method proposed by T. Pevny and J.Fridrich. The experimental results show that the proposed method has less detectability compared to MME (modified matrix encoding).